TR-Dizin İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8652
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Article Citation - WoS: 5Citation - Scopus: 5On Some Fractional Operators Generated From Abel's Formula(Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, EkinThis work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.Article Citation - WoS: 13Citation - Scopus: 15Hardy-Copson Type Inequalities for Nabla Time Scale Calculus(Tubitak Scientific & Technological Research Council Turkey, 2021) Kaymakcalan, Billur; Kayar, ZeynepThis paper is devoted to the nabla unification of the discrete and continuous Hardy?Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.Article Citation - WoS: 2Citation - Scopus: 6Diamond Alpha Hardy-Copson Type Dynamic Inequalities(Hacettepe Univ, Fac Sci, 2022) Kaymakcalan, Billur; Kayar, ZeynepIn this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.Article Citation - WoS: 11Citation - Scopus: 12Diagnosis of Osteoarthritic Changes, Loss of Cervical Lordosis, and Disc Space Narrowing on Cervical Radiographs With Deep Learning Methods(Turkish Joint Diseases Foundation, 2022) Tokdemir, Gul; Ureten, Kemal; Atalar, Ebru; Duran, Semra; Maras, Hakan; Maras, YukselObjectives: In this study, we aimed to differentiate normal cervical graphs and graphs of diseases that cause mechanical neck pain by using deep convolutional neural networks (DCNN) technology. Materials and methods: In this retrospective study, the convolutional neural networks were used and transfer learning method was applied with the pre-trained VGG-16, VGG-19, Resnet-101, and DenseNet-201 networks. Our data set consisted of 161 normal lateral cervical radiographs and 170 lateral cervical radiographs with osteoarthritis and cervical degenerative disc disease. Results: We compared the performances of the classification models in terms of performance metrics such as accuracy,Article Citation - WoS: 9Citation - Scopus: 11The Diagnosis of Femoroacetabular Impingement Can Be Made on Pelvis Radiographs Using Deep Learning Methods(Turkish Joint Diseases Foundation, 2023) Atalar, Ebru; Ureten, Kemal; Kanatli, Ulunay; Ciceklidag, Murat; Kaya, Ibrahim; Vural, Abdurrahman; Maras, YukselObjectives: The aim of this study was to evaluate diagnostic ability of deep learning models, particularly convolutional neural network models used for image classification, for femoroacetabular impingement (FAI) using hip radiographs. Materials and methods: Between January 2010 and December 2020, pelvic radiographs of a total of 516 patients (270 males, 246 females; mean age: 39.1 +/- 3.8 years; range, 20 to 78 years) with hip pain were retrospectively analyzed. Based on inclusion and exclusion criteria, a total of 888 hip radiographs (308 diagnosed with FAI and 508 considered normal) were evaluated using deep learning methods. Pre-trained VGG-16, ResNet-101, MobileNetV2, and Inceptionv3 models were used for transfer learning. Results: As assessed by performance measures such as accuracy, sensitivity, specificity, precision, F-1 score, and area under the curve (AUC), the VGG-16 model outperformed other pre-trained networks in diagnosing FAI. With the pre-trained VGG-16 model, the results showed 86.6% accuracy, 82.5% sensitivity, 89.6% specificity, 85.5% precision, 83.9% F1 score, and 0.92 AUC. Conclusion: In patients with suspected FAI, pelvic radiography is the first imaging method to be applied, and deep learning methods can help in the diagnosis of this syndrome.Article Citation - WoS: 3Citation - Scopus: 3Left-Definite Hamiltonian Systems and Corresponding Nested Circles(Tubitak Scientific & Technological Research Council Turkey, 2023) Ugurlu, EkinThis work aims to construct the Titchmarsh-Weyl M(A)-theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter A. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.Article Citation - WoS: 3Citation - Scopus: 3The Lebesgue Constants on Projective Spaces(Tubitak, 2021) Kushpel, AlexanderWe give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgueconstants or norms of the Fourier-Laplace projections on the real projective spaces Pd(R). In particular, these resultsextend sharp asymptotic found by Fejer [2] in the case of S1in 1910 and by Gronwall [4] in 1914 in the case of S2. Thecase of spheres, Sd, complex and quaternionic projective spaces, Pd(C), Pd(H) and the Cayley elliptic plane P16(Cay)was considered by Kushpel [8].Article Citation - Scopus: 5Structural Forms and Energies of NiN, N=12-14, Clusters(Assoc Sci Res, 1999) Güvenç, Ziya B.; Güvenç, Dilek; Jellinek, JuliusEquilibrium structural forms of the $Ni_n$, n=12-14, clusters, as defined by an embedded-atom potential, are obtained using molecular dynamics and thermal quenching simulations. The isomers (locally stable geometric forms) are distinguished from those stationary structures that correspond to saddle points of the potential energy surface. Isomer statistics are obtained using a large number of initial quenching configurations generated along high-energy trajectories (the energies are high enough to "melt" the clusters). Probabilities of sampling the basins of attraction of the different isomers are computed and the spectra of their energies are analyzed.Article Citation - WoS: 1Scattering and Characteristic Functions of a Dissipative Operator Generated by a System of Equations(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Bayram, Elgiz; Tas, KenanIn this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foias model operator theory we prove a completeness theorem.Article On a Fifth-Order Nonselfadjoint Boundary Value Problem(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, KenanIn this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative
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